[ebot] Consolidate database connection pooling

[ewlarson]

Summary

Consolidates SQLAlchemy engine and session creation behind shared app-level helpers so request-path code does not create independent PostgreSQL pools per module/service.

Why

AppSignal reported asyncpg.exceptions.TooManyConnectionsError before production launch. The root issue was broader than one endpoint: multiple request paths could construct their own engines/sessionmakers, multiplying pool counts across API workers.

What changed

• Added shared async/sync engine factories and db.session.
• • Rewired request-path modules and services to use shared engines/sessions.
• • Disposes shared engines during FastAPI lifespan shutdown.
• • Shortens DB connection hold time in resource detail/list and search rendering.
• • Skips expensive similar-item enrichment on resource list responses.
• • Preserves licensed-access response behavior from develop using short-lived sessions where needed.
• • Documents the connection-pool policy and perf-test expectations.

Validation

• uv run ruff check on touched API/resource/search/utils files: passed.
• • python -m compileall on conflict-touched files: passed.
• • Focused pytest after rebase: 12 passed for resource detail/list/search, JSON:API licensed access serialization, licensed access repository, and similar items.
• • Reran resource list unit test with endpoint cache disabled: 1 passed. The combined run first hit a stale Redis endpoint-cache fixture record against a dummy request object, not application code.
• • Earlier branch validation: API-only make k6-smoke passed; API-only make k6-stress passed with 0 failures and no TooManyConnections, SQLAlchemy pool timeout, asyncpg, or HTTP 500 log matches.